Question

$4$men and $6$ women can complete a work in $8$ days, while $3$ men and $7$ women can complete it in $10$ days. In how many days will $10$ women complete it?

• A. $35$
• B. $40$
• C. $45$
• D. $50$

Answer 1

The correct option is B $40$

Let $1$ man's $1$ day's work $=x$ and $1$ woman's $1$ day's work $=y$.
Then, $4x+6y=\frac{1}{8}$ and $3x+7y=\frac{1}{10}$.
Solving the two equations, we get: $x=\frac{11}{400},y=\frac{1}{400}$
$\therefore$ $1$ woman's $1$ day's work $=\frac{1}{400}$.
$\Rightarrow$ $10$ women's $1$ day's work $=(\frac{1}{400}\times 10)=\frac{1}{40}$.
Hence, $10$ women will complete the work in $40$ days.